%matplotlib notebook

import seaborn as sns
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import rankdata
from IPython.display import display, display_markdown

def display_md(md, **kwargs):
    return display_markdown(md, raw=True, **kwargs)

sns.set(style='whitegrid', palette='Set2')

# unigram
df_uni = pd.read_csv('dedup.en.words.unigrams.tsv', sep='\t')
total_unigrams = df_uni['unigram_freq'].sum()
display_md(f'Total number of unigrams: {total_unigrams}')
df_uni['unigram_freq'] = df_uni['unigram_freq'] / total_unigrams
df_uni['log_unigram_freq'] = np.log10(df_uni['unigram_freq'])
df_uni = df_uni.drop(columns='unigram_freq')
display(df_uni.head())

Total number of unigrams: 750595864

	unigram	log_unigram_freq
0	the	-1.447468
1	you	-1.464249
2	i	-1.476922
3	to	-1.588910
4	a	-1.670625

# bigram
df_bi = pd.read_csv('dedup.en.words.bigrams.tsv', sep='\t')
total_bigrams = df_bi['bigram_freq'].sum()
df_bi = df_bi[df_bi['bigram_freq'] > 1]
display_md(f'Total number of bigrams: {total_bigrams} (we threw some low-frequency ones away)')
df_bi['bigram_freq'] = df_bi['bigram_freq'] / total_unigrams
df_bi['log_bigram_freq'] = np.log10(df_bi['bigram_freq'])
df_bi = df_bi.drop(columns='bigram_freq')
display(df_bi.head())

Total number of bigrams: 659315676 (we threw some low-frequency ones away)

	bigram	log_bigram_freq
0	i m	-2.320121
1	it s	-2.342565
2	don t	-2.370733
3	you re	-2.530850
4	in the	-2.539749

# word1/word2
df_bi['word1'] = df_bi['bigram'].apply(lambda x: x.split(' ')[0])
df_bi['word2'] = df_bi['bigram'].apply(lambda x: x.split(' ')[1])
df_bi = df_bi.merge(df_uni.rename(columns={'unigram': 'word1', 'log_unigram_freq': 'log_word1_freq'}), how='left', on='word1')
df_bi = df_bi.merge(df_uni.rename(columns={'unigram': 'word2', 'log_unigram_freq': 'log_word2_freq'}), how='left', on='word2')
display(df_bi.head())

	bigram	log_bigram_freq	word1	word2	log_word1_freq	log_word2_freq
0	i m	-2.320121	i	m	-1.476922	-2.307584
1	it s	-2.342565	it	s	-1.799641	-1.771602
2	don t	-2.370733	don	t	-2.364607	-1.939389
3	you re	-2.530850	you	re	-1.464249	-2.289862
4	in the	-2.539749	in	the	-1.941774	-1.447468

# ftp/btp
df_bi['log_ftp'] = df_bi['log_bigram_freq'] - df_bi['log_word1_freq']
df_bi['log_btp'] = df_bi['log_bigram_freq'] - df_bi['log_word2_freq']
df_bi['pmi'] = df_bi['log_bigram_freq'] - df_bi['log_word1_freq'] - df_bi['log_word2_freq']
display(df_bi.head())

	bigram	log_bigram_freq	word1	word2	log_word1_freq	log_word2_freq	log_ftp	log_btp	pmi
0	i m	-2.320121	i	m	-1.476922	-2.307584	-0.843199	-0.012538	1.464385
1	it s	-2.342565	it	s	-1.799641	-1.771602	-0.542925	-0.570963	1.228678
2	don t	-2.370733	don	t	-2.364607	-1.939389	-0.006126	-0.431344	1.933263
3	you re	-2.530850	you	re	-1.464249	-2.289862	-1.066602	-0.240988	1.223261
4	in the	-2.539749	in	the	-1.941774	-1.447468	-0.597975	-1.092281	0.849493

# store df
df_bi.to_csv('full_bigram_data.tsv', sep='\t', index=False)

# load df
df_bi = pd.read_csv('full_bigram_data.tsv', sep='\t')

g = sns.PairGrid(df_bi)
g = g.map_diag(plt.hist)

def hexbin(x, y, color, **kwargs):
    cmap = sns.light_palette(color, as_cmap=True)
    plt.hexbin(x, y, gridsize=15, cmap=cmap, **kwargs)

g = g.map_offdiag(hexbin)

g = sns.distplot(df_uni['log_unigram_freq'], kde=False)
g.set(yscale='log');

g = sns.distplot(df_bi['log_bigram_freq'], kde=False)
g.set(yscale='log');

x = df_bi['log_word1_freq']
y = df_bi['log_word2_freq']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_word1_freq']
y = df_bi['log_bigram_freq']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_word2_freq']
y = df_bi['log_bigram_freq']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_word1_freq']
y = df_bi['log_ftp']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_word2_freq']
y = df_bi['log_ftp']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_word1_freq']
y = df_bi['log_btp']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_word2_freq']
y = df_bi['log_btp']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_ftp']
y = df_bi['log_btp']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_ftp']
y = df_bi['pmi']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_btp']
y = df_bi['pmi']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_word1_freq']
y = df_bi['pmi']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

x = df_bi['log_word2_freq']
y = df_bi['pmi']
g = sns.jointplot(x, y, kind='hex', alpha=.8)
sns.regplot(x, y, ax=g.ax_joint, scatter=False, ci=None, color='black');

ev_btp = np.sum(df_bi['log_word1_freq'] * df_bi['log_btp'])
display_md(f'EV for BTP: {ev_btp.round(2)}')
ev_ftp = np.sum(df_bi['log_word2_freq'] * df_bi['log_ftp'])
display_md(f'EV for FTP: {ev_ftp.round(2)}')

EV for BTP: 225091352.81

EV for FTP: 233842682.7

# convert this Jupyter notebook
import subprocess as sp
make_md = 'jupyter nbconvert transitional_probabilities.ipynb --to html --output transitional_probabilities.html'.split(' ')
convert = sp.run(make_md)
if convert.returncode == 0:
    display_md('Jupyter notebook converted successfully.')
else:
    display_md('Error: encountered problem converting Jupyter notebook')

Jupyter notebook converted successfully.